When genetic epidemiology meets psychiatry, the problems become immense. Genetic linkage analysis and segregation analysis in theory represent two powerful tools for identifying specific genes, detecting genetic heterogeneity, and predicting recurrence risk, but the problems in using these techniques in psychiatric disease have become more evident as investigators try to apply them. Several major psychiatric diseases show strong evidence that genes are involved in disease expression, but family data do not fit simple patterns of Mendelian inheritance. Genetic linkage analysis has failed to reproducibly identify a gene locus for any psychiatric disease. We confront new problems in the genetic analysis of psychiatric disease, including, among other things: heterogeneity of psychiatric disease and the limitations of current methodology in dealing with it; the effect of family sampling on genetic studies; the limited number of inheritance models used in genetic analysis; ambiguous phenotype definition; and the informativeness of families for linkage analysis. We will investigate problems in the mathematical foundation of current methods and in their application to psychiatric disease. Using both analytical approaches and computer simulation techniques, we will develop and test new methodologies in the genetic analysis of psychiatric disease. the results of our work will have a practical impact on real data collection and analysis. We aim to apply the results of our work to common psychiatric diseases with genetic components, diseases such as schizophrenia, Alzheimer's disease, and panic disorder. Greater understanding of the genetic contributions to psychiatric disease will lead in turn to improved counseling, treatment, and, eventually, prevention. Specifically, we will investigate the following problems: (I) Two-locus and multilocus models are of increasing importance for a number of human diseases. Part I examines linkage analysis of two-locus models and will evaluate single-locus approximations for these analyses. (II) How families are selected ("ascertained") for segregation analysis can profoundly affect the results of that analysis, yet how to correct for ascertainment remains a difficult, only partly solved problem. Part II develops a new nonparametric correction and considers three other critical ascertainment problems as well. (III) Complications arise when linkage analysis is performed on complex psychiatric diseases. Part III focuses on linkage strategies, including within-family heterogeneity, between-family heterogeneity, informativeness of different types of pedigrees, and the sensitivity of lod scores to changes in phenotypes. (IV) Finally, Part IV deals with reduced penetrance and affecteds-only methods of linkage analysis. Throughout, the work will both (a) determine the extent of problems, and (b) develop and test solutions to these problems. Solutions and their testing will require both theoretical tools and computer simulation.